{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c93b1b70",
   "metadata": {},
   "source": [
    "# Optional Lab: Feature Engineering and Polynomial Regression\n",
    "\n",
    "![](./images/C1_W2_Lab07_FeatureEngLecture.PNG)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d305214",
   "metadata": {},
   "source": [
    "## Goals\n",
    "In this lab you will:\n",
    "- explore feature engineering and polynomial regression which allows you to use the machinery of linear regression to fit very complicated, even very non-linear functions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9406d8d",
   "metadata": {},
   "source": [
    "## Tools\n",
    "You will utilize the function developed in previous labs as well as matplotlib and NumPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "35f3326f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:05.379329Z",
     "start_time": "2022-06-17T05:05:04.177193Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from lab_utils_multi import zscore_normalize_features, run_gradient_descent_feng\n",
    "np.set_printoptions(precision=2)  # reduced display precision on numpy arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2435db4",
   "metadata": {},
   "source": [
    "<a name='FeatureEng'></a>\n",
    "# Feature Engineering and Polynomial Regression Overview\n",
    "\n",
    "Out of the box, linear regression provides a means of building models of the form:\n",
    "$$f_{\\mathbf{w},b} = w_0x_0 + w_1x_1+ ... + w_{n-1}x_{n-1} + b \\tag{1}$$ \n",
    "What if your features/data are non-linear or are combinations of features? For example,  Housing prices do not tend to be linear with living area but penalize very small or very large houses resulting in the curves shown in the graphic above. How can we use the machinery of linear regression to fit this curve? Recall, the 'machinery' we have is the ability to modify the parameters $\\mathbf{w}$, $\\mathbf{b}$ in (1) to 'fit' the equation to the training data. However, no amount of adjusting of $\\mathbf{w}$,$\\mathbf{b}$ in (1) will achieve a fit to a non-linear curve.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68c231f",
   "metadata": {},
   "source": [
    "<a name='PolynomialFeatures'></a>\n",
    "## Polynomial Features\n",
    "\n",
    "Above we were considering a scenario where the data was non-linear. Let's try using what we know so far to fit a non-linear curve. We'll start with a simple quadratic: $y = 1+x^2$\n",
    "\n",
    "You're familiar with all the routines we're using. They are available in the lab_utils.py file for review. We'll use [`np.c_[..]`](https://numpy.org/doc/stable/reference/generated/numpy.c_.html) which is a NumPy routine to concatenate along the column boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "71fe7a55",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:05.635389Z",
     "start_time": "2022-06-17T05:05:05.381332Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration         0, Cost: 1.65756e+03\n",
      "Iteration       100, Cost: 6.94549e+02\n",
      "Iteration       200, Cost: 5.88475e+02\n",
      "Iteration       300, Cost: 5.26414e+02\n",
      "Iteration       400, Cost: 4.90103e+02\n",
      "Iteration       500, Cost: 4.68858e+02\n",
      "Iteration       600, Cost: 4.56428e+02\n",
      "Iteration       700, Cost: 4.49155e+02\n",
      "Iteration       800, Cost: 4.44900e+02\n",
      "Iteration       900, Cost: 4.42411e+02\n",
      "w,b found by gradient descent: w: [18.7], b: -52.0834\n",
      "Iteration         0, Cost: 1.65756e+03\n",
      "Iteration       100, Cost: 6.94549e+02\n",
      "Iteration       200, Cost: 5.88475e+02\n",
      "Iteration       300, Cost: 5.26414e+02\n",
      "Iteration       400, Cost: 4.90103e+02\n",
      "Iteration       500, Cost: 4.68858e+02\n",
      "Iteration       600, Cost: 4.56428e+02\n",
      "Iteration       700, Cost: 4.49155e+02\n",
      "Iteration       800, Cost: 4.44900e+02\n",
      "Iteration       900, Cost: 4.42411e+02\n",
      "w,b found by gradient descent: w: [18.7], b: -52.0834\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create target data\n",
    "x = np.arange(0, 20, 1)\n",
    "y = 1 + x**2\n",
    "X = x.reshape(-1, 1)\n",
    "\n",
    "model_w,model_b = run_gradient_descent_feng(X,y,iterations=1000, alpha = 1e-2)\n",
    "\n",
    "plt.scatter(x, y, marker='x', c='r', label=\"Actual Value\"); plt.title(\"no feature engineering\")\n",
    "plt.plot(x,X@model_w + model_b, label=\"Predicted Value\");  plt.xlabel(\"X\"); plt.ylabel(\"y\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c8d7c8",
   "metadata": {},
   "source": [
    "Well, as expected, not a great fit. What is needed is something like $y= w_0x_0^2 + b$, or a **polynomial feature**.\n",
    "To accomplish this, you can modify the *input data* to *engineer* the needed features. If you swap the original data with a version that squares the $x$ value, then you can achieve $y= w_0x_0^2 + b$. Let's try it. Swap `X` for `X**2` below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "01d92882",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:05.651438Z",
     "start_time": "2022-06-17T05:05:05.637391Z"
    }
   },
   "outputs": [],
   "source": [
    "# create target data\n",
    "x = np.arange(0, 20, 1)\n",
    "y = 1 + x**2\n",
    "\n",
    "# Engineer features \n",
    "X = x**2      #<-- added engineered feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a295f0dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:06.716183Z",
     "start_time": "2022-06-17T05:05:05.654424Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration         0, Cost: 7.32922e+03\n",
      "Iteration      1000, Cost: 2.24844e-01\n",
      "Iteration      2000, Cost: 2.22795e-01\n",
      "Iteration         0, Cost: 7.32922e+03\n",
      "Iteration      1000, Cost: 2.24844e-01\n",
      "Iteration      2000, Cost: 2.22795e-01\n",
      "Iteration      3000, Cost: 2.20764e-01\n",
      "Iteration      4000, Cost: 2.18752e-01\n",
      "Iteration      5000, Cost: 2.16758e-01\n",
      "Iteration      3000, Cost: 2.20764e-01\n",
      "Iteration      4000, Cost: 2.18752e-01\n",
      "Iteration      5000, Cost: 2.16758e-01\n",
      "Iteration      6000, Cost: 2.14782e-01\n",
      "Iteration      7000, Cost: 2.12824e-01\n",
      "Iteration      8000, Cost: 2.10884e-01\n",
      "Iteration      6000, Cost: 2.14782e-01\n",
      "Iteration      7000, Cost: 2.12824e-01\n",
      "Iteration      8000, Cost: 2.10884e-01\n",
      "Iteration      9000, Cost: 2.08962e-01\n",
      "w,b found by gradient descent: w: [1.], b: 0.0490\n",
      "Iteration      9000, Cost: 2.08962e-01\n",
      "w,b found by gradient descent: w: [1.], b: 0.0490\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = X.reshape(-1, 1)  #X should be a 2-D Matrix\n",
    "model_w,model_b = run_gradient_descent_feng(X, y, iterations=10000, alpha = 1e-5)\n",
    "\n",
    "plt.scatter(x, y, marker='x', c='r', label=\"Actual Value\"); plt.title(\"Added x**2 feature\")\n",
    "plt.plot(x, np.dot(X,model_w) + model_b, label=\"Predicted Value\"); plt.xlabel(\"x\"); plt.ylabel(\"y\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ead9889",
   "metadata": {},
   "source": [
    "Great! near perfect fit. Notice the values of $\\mathbf{w}$ and b printed right above the graph: `w,b found by gradient descent: w: [1.], b: 0.0490`. Gradient descent modified our initial values of $\\mathbf{w},b $ to be (1.0,0.049) or a model of $y=1*x_0^2+0.049$, very close to our target of $y=1*x_0^2+1$. If you ran it longer, it could be a better match. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24f56e3b",
   "metadata": {},
   "source": [
    "### Selecting Features\n",
    "<a name='GDF'></a>\n",
    "Above, we knew that an $x^2$ term was required. It may not always be obvious which features are required. One could add a variety of potential features to try and find the most useful. For example, what if we had instead tried : $y=w_0x_0 + w_1x_1^2 + w_2x_2^3+b$ ? \n",
    "\n",
    "Run the next cells. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "76d7829e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:06.732183Z",
     "start_time": "2022-06-17T05:05:06.718186Z"
    }
   },
   "outputs": [],
   "source": [
    "# create target data\n",
    "x = np.arange(0, 20, 1)\n",
    "y = x**2\n",
    "\n",
    "# engineer features .\n",
    "X = np.c_[x, x**2, x**3]   #<-- added engineered feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d5dd1377",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:07.808300Z",
     "start_time": "2022-06-17T05:05:06.734184Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration         0, Cost: 1.14029e+03\n",
      "Iteration      1000, Cost: 3.28539e+02\n",
      "Iteration      2000, Cost: 2.80443e+02\n",
      "Iteration         0, Cost: 1.14029e+03\n",
      "Iteration      1000, Cost: 3.28539e+02\n",
      "Iteration      2000, Cost: 2.80443e+02\n",
      "Iteration      3000, Cost: 2.39389e+02\n",
      "Iteration      4000, Cost: 2.04344e+02\n",
      "Iteration      5000, Cost: 1.74430e+02\n",
      "Iteration      3000, Cost: 2.39389e+02\n",
      "Iteration      4000, Cost: 2.04344e+02\n",
      "Iteration      5000, Cost: 1.74430e+02\n",
      "Iteration      6000, Cost: 1.48896e+02\n",
      "Iteration      7000, Cost: 1.27100e+02\n",
      "Iteration      8000, Cost: 1.08495e+02\n",
      "Iteration      6000, Cost: 1.48896e+02\n",
      "Iteration      7000, Cost: 1.27100e+02\n",
      "Iteration      8000, Cost: 1.08495e+02\n",
      "Iteration      9000, Cost: 9.26132e+01\n",
      "w,b found by gradient descent: w: [0.08 0.54 0.03], b: 0.0106\n",
      "Iteration      9000, Cost: 9.26132e+01\n",
      "w,b found by gradient descent: w: [0.08 0.54 0.03], b: 0.0106\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_w,model_b = run_gradient_descent_feng(X, y, iterations=10000, alpha=1e-7)\n",
    "\n",
    "plt.scatter(x, y, marker='x', c='r', label=\"Actual Value\"); plt.title(\"x, x**2, x**3 features\")\n",
    "plt.plot(x, X@model_w + model_b, label=\"Predicted Value\"); plt.xlabel(\"x\"); plt.ylabel(\"y\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1d82719",
   "metadata": {},
   "source": [
    "Note the value of $\\mathbf{w}$, `[0.08 0.54 0.03]` and b is `0.0106`.This implies the model after fitting/training is:\n",
    "$$ 0.08x + 0.54x^2 + 0.03x^3 + 0.0106 $$\n",
    "Gradient descent has emphasized the data that is the best fit to the $x^2$ data by increasing the $w_1$ term relative to the others.  If you were to run for a very long time, it would continue to reduce the impact of the other terms. \n",
    ">Gradient descent is picking the 'correct' features for us by emphasizing its associated parameter\n",
    "\n",
    "Let's review this idea:\n",
    "- Intially, the features were re-scaled so they are comparable to each other\n",
    "- less weight value implies less important/correct feature, and in extreme, when the weight becomes zero or very close to zero, the associated feature useful in fitting the model to the data.\n",
    "- above, after fitting, the weight associated with the $x^2$ feature is much larger than the weights for $x$ or $x^3$ as it is the most useful in fitting the data. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43045305",
   "metadata": {},
   "source": [
    "### An Alternate View\n",
    "Above, polynomial features were chosen based on how well they matched the target data. Another way to think about this is to note that we are still using linear regression once we have created new features. Given that, the best features will be linear relative to the target. This is best understood with an example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cb41c021",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:07.823945Z",
     "start_time": "2022-06-17T05:05:07.810302Z"
    }
   },
   "outputs": [],
   "source": [
    "# create target data\n",
    "x = np.arange(0, 20, 1)\n",
    "y = x**2\n",
    "\n",
    "# engineer features .\n",
    "X = np.c_[x, x**2, x**3]   #<-- added engineered feature\n",
    "X_features = ['x','x^2','x^3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "823934c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:08.092026Z",
     "start_time": "2022-06-17T05:05:07.824945Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1, 3, figsize=(12, 3), sharey=True)\n",
    "for i in range(len(ax)):\n",
    "    ax[i].scatter(X[:,i],y)\n",
    "    ax[i].set_xlabel(X_features[i])\n",
    "ax[0].set_ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aecdffb",
   "metadata": {},
   "source": [
    "Above, it is clear that the $x^2$ feature mapped against the target value $y$ is linear. Linear regression can then easily generate a model using that feature."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f34bcc",
   "metadata": {},
   "source": [
    "### Scaling features\n",
    "As described in the last lab, if the data set has features with significantly different scales, one should apply feature scaling to speed gradient descent. In the example above, there is $x$, $x^2$ and $x^3$ which will naturally have very different scales. Let's apply Z-score normalization to our example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d4dd7dfd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:08.108021Z",
     "start_time": "2022-06-17T05:05:08.094027Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak to Peak range by column in Raw        X:[  19  361 6859]\n",
      "Peak to Peak range by column in Normalized X:[3.3  3.18 3.28]\n",
      "Peak to Peak range by column in Raw        X:[  19  361 6859]\n",
      "Peak to Peak range by column in Normalized X:[3.3  3.18 3.28]\n"
     ]
    }
   ],
   "source": [
    "# create target data\n",
    "x = np.arange(0,20,1)\n",
    "X = np.c_[x, x**2, x**3]\n",
    "print(f\"Peak to Peak range by column in Raw        X:{np.ptp(X,axis=0)}\")\n",
    "\n",
    "# add mean_normalization \n",
    "X = zscore_normalize_features(X)     \n",
    "print(f\"Peak to Peak range by column in Normalized X:{np.ptp(X,axis=0)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b75e33d5",
   "metadata": {},
   "source": [
    "Now we can try again with a more aggressive value of alpha:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "85dadadf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:10.764029Z",
     "start_time": "2022-06-17T05:05:08.110024Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration         0, Cost: 9.42147e+03\n",
      "Iteration         0, Cost: 9.42147e+03\n",
      "Iteration     10000, Cost: 3.90938e-01\n",
      "Iteration     10000, Cost: 3.90938e-01\n",
      "Iteration     20000, Cost: 2.78389e-02\n",
      "Iteration     20000, Cost: 2.78389e-02\n",
      "Iteration     30000, Cost: 1.98242e-03\n",
      "Iteration     30000, Cost: 1.98242e-03\n",
      "Iteration     40000, Cost: 1.41169e-04\n",
      "Iteration     40000, Cost: 1.41169e-04\n",
      "Iteration     50000, Cost: 1.00527e-05\n",
      "Iteration     50000, Cost: 1.00527e-05\n",
      "Iteration     60000, Cost: 7.15855e-07\n",
      "Iteration     60000, Cost: 7.15855e-07\n",
      "Iteration     70000, Cost: 5.09763e-08\n",
      "Iteration     70000, Cost: 5.09763e-08\n",
      "Iteration     80000, Cost: 3.63004e-09\n",
      "Iteration     80000, Cost: 3.63004e-09\n",
      "Iteration     90000, Cost: 2.58497e-10\n",
      "Iteration     90000, Cost: 2.58497e-10\n",
      "w,b found by gradient descent: w: [5.27e-05 1.13e+02 8.43e-05], b: 123.5000\n",
      "w,b found by gradient descent: w: [5.27e-05 1.13e+02 8.43e-05], b: 123.5000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,20,1)\n",
    "y = x**2\n",
    "\n",
    "X = np.c_[x, x**2, x**3]\n",
    "X = zscore_normalize_features(X) \n",
    "\n",
    "model_w, model_b = run_gradient_descent_feng(X, y, iterations=100000, alpha=1e-1)\n",
    "\n",
    "plt.scatter(x, y, marker='x', c='r', label=\"Actual Value\"); plt.title(\"Normalized x x**2, x**3 feature\")\n",
    "plt.plot(x,X@model_w + model_b, label=\"Predicted Value\"); plt.xlabel(\"x\"); plt.ylabel(\"y\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1ffc93d",
   "metadata": {},
   "source": [
    "Feature scaling allows this to converge much faster.   \n",
    "Note again the values of $\\mathbf{w}$. The $w_1$ term, which is the $x^2$ term is the most emphasized. Gradient descent has all but eliminated the $x^3$ term."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93b87a2b",
   "metadata": {},
   "source": [
    "### Complex Functions\n",
    "With feature engineering, even quite complex functions can be modeled:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fb8c5b2f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T05:05:28.841169Z",
     "start_time": "2022-06-17T05:05:10.767032Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration         0, Cost: 2.24887e-01\n",
      "Iteration         0, Cost: 2.24887e-01\n",
      "Iteration    100000, Cost: 2.31061e-02\n",
      "Iteration    100000, Cost: 2.31061e-02\n",
      "Iteration    200000, Cost: 1.83619e-02\n",
      "Iteration    200000, Cost: 1.83619e-02\n",
      "Iteration    300000, Cost: 1.47950e-02\n",
      "Iteration    300000, Cost: 1.47950e-02\n",
      "Iteration    400000, Cost: 1.21114e-02\n",
      "Iteration    400000, Cost: 1.21114e-02\n",
      "Iteration    500000, Cost: 1.00914e-02\n",
      "Iteration    500000, Cost: 1.00914e-02\n",
      "Iteration    600000, Cost: 8.57025e-03\n",
      "Iteration    600000, Cost: 8.57025e-03\n",
      "Iteration    700000, Cost: 7.42385e-03\n",
      "Iteration    700000, Cost: 7.42385e-03\n",
      "Iteration    800000, Cost: 6.55908e-03\n",
      "Iteration    800000, Cost: 6.55908e-03\n",
      "Iteration    900000, Cost: 5.90594e-03\n",
      "Iteration    900000, Cost: 5.90594e-03\n",
      "w,b found by gradient descent: w: [-1.61e+00 -1.01e+01  3.00e+01 -6.92e-01 -2.37e+01 -1.51e+01  2.09e+01\n",
      " -2.29e-03 -4.69e-03  5.51e-02  1.07e-01 -2.53e-02  6.49e-02], b: -0.0073\n",
      "w,b found by gradient descent: w: [-1.61e+00 -1.01e+01  3.00e+01 -6.92e-01 -2.37e+01 -1.51e+01  2.09e+01\n",
      " -2.29e-03 -4.69e-03  5.51e-02  1.07e-01 -2.53e-02  6.49e-02], b: -0.0073\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,20,1)\n",
    "y = np.cos(x/2)\n",
    "\n",
    "X = np.c_[x, x**2, x**3,x**4, x**5, x**6, x**7, x**8, x**9, x**10, x**11, x**12, x**13]\n",
    "X = zscore_normalize_features(X) \n",
    "\n",
    "model_w,model_b = run_gradient_descent_feng(X, y, iterations=1000000, alpha = 1e-1)\n",
    "\n",
    "plt.scatter(x, y, marker='x', c='r', label=\"Actual Value\"); plt.title(\"Normalized x x**2, x**3 feature\")\n",
    "plt.plot(x,X@model_w + model_b, label=\"Predicted Value\"); plt.xlabel(\"x\"); plt.ylabel(\"y\"); plt.legend(); plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c57adced",
   "metadata": {},
   "source": [
    "\n",
    "## Congratulations!\n",
    "In this lab you:\n",
    "- learned how linear regression can model complex, even highly non-linear functions using feature engineering\n",
    "- recognized that it is important to apply feature scaling when doing feature engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21bdc041",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ec9ccb5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8fe3e0ff",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b324424",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7972c64a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "toc-autonumbering": false
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
